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Question 326778: Suppose the demand and price for the HBO cable channel are related by p=-.5q+30.95, where p is the monthly price in dollars and q is measured in millions of subscribers. If the price and supply are related by p=.3q+2.15, what are the equilibrium quality and price?
Help I am lost!!!
Answer by jessica43(140)   (Show Source):
You can put this solution on YOUR website! The equilibrium price and quantity occurs when the demand equals the supply. At equilibrium, both demand and supply have the same price and same quantity. So since both equations have the same value for P at equilibrium, and both equations equal P, you can set them equal to each other:
-0.5Q + 30.95 = P = 0.3Q + 2.15
Now solve for Q by combining like terms:
-0.5Q + 30.95 = 0.3Q + 2.15 (now subtract 2.15 from each side)
-0.5Q + 28.8 = 0.3Q (now add 0.5Q to each side)
28.8 = 0.8Q (now divided each side by 0.8)
36 = Q
So your equilibrium quantity is 36. Now plug this into either the demand or the supply equations to find P. Using either equation will get you the same answer - I am just choosing to use the demand equation.
P = -0.5Q + 30.95
P = -0.5(36) + 30.95
P = -18 + 30.95
P = 12.95
So the equilibrium price is $12.95.
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